Is there a way to get the dimensions of the camera?
As far as I know camera objects don't have geometry, and hence no real world Blender Units dimensions.
The viewport size of a camera object depends on a variety of combined factors.

The camera object size reflects the render resolution set in the
render properties panel, changing proportions according to the image
size.
Visual scaling factor, controlled by the Size property in the Object Data panel &gt; Viewport Display &gt; Size.
The Focal Length will also affect the camera shape by adjusting the angle of the sides to reflect the current view field.
Lastly the Camera Shift X and Shift Y properties will skew its shape to reflect the applied panning effect.


As pointed out by Jaroslav Jerryno Novotny you can get camera corners from the python API with camera_obj.data.view_frame.
For more info see https://blender.stackexchange.com/a/28561/7777